LMI-BASED ASYMPTOTIC STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (03) ◽  
pp. 257-265 ◽  
Author(s):  
TAO LI ◽  
CHANGYIN SUN ◽  
XIANLIN ZHAO ◽  
CHONG LIN
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Activation Functions ◽  
Different Types ◽  
Conservative Result

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

scholarly journals On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

scholarly journals Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

Global Asymptotic Stability of Stochastic Fuzzy Cellular Neural Networks with Time-Varying Delays

2010 ◽  
Vol 139-141 ◽  
pp. 1714-1717
Author(s):  
Wen Guang Luo ◽  
Yong Hua Liu ◽  
Hong Li Lan
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
The Stability ◽  
Delay Dependent

In this paper, the problem of global asymptotic stability in the mean square for stochastic fuzzy cellular neural networks (SFCNN) with time-varying delays is investigated. By constructing a newly proposed Lyapunov-Krasovskii function (LKF) and using Ito’s stochastic stability theory, a novel delay-dependent stability criterion is derived. The obtained stability result is helpful to design the stability of fuzzy cellular neural networks (FCNN) with time-varying delays when stochastic noise is taken into consideration. Since it is presented in terms of a linear matrix inequality (LMI), the sufficient condition is easy to be checked efficiently by utilizing some standard numerical packages such as the LMI Control Toolbox in Matlab. Finally, an illustrate example is given to verify the feasibility and usefulness of the proposed result.

DELAY-DEPENDENT ASYMPTOTIC STABILITY OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (01) ◽  
pp. 245-250 ◽  
Author(s):  
SHENGYUAN XU ◽  
JAMES LAM ◽  
DANIEL W. C. HO
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Condition ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Unique Equilibrium ◽  
Delay Dependent ◽  
Asymptotic Stability Condition

This paper considers the problem of stability analysis for neural networks with time-varying delays. The time-varying delays under consideration are assumed to be bounded but not necessarily differentiable. In terms of a linear matrix inequality, a delay-dependent asymptotic stability condition is developed, which ensures the existence of a unique equilibrium point and its global asymptotic stability. The proposed stability condition is easy to check and less conservative. An example is provided to show the effectiveness of the proposed condition.

scholarly journals LMI-Based Criterion for the Robust Stability of 2D Discrete State-Delayed Systems Using Generalized Overflow Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Anurita Dey ◽  
Haranath Kar
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
2D Systems ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Delayed Systems ◽  
Discrete State ◽  
Special Cases ◽  
New Criterion

This paper addresses the problem of global asymptotic stability of a class of discrete uncertain state-delayed systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model using generalized overflow nonlinearities. The uncertainties are assumed to be norm bounded. A computationally tractable, that is, linear-matrix-inequality-(LMI-) based new criterion for the global asymptotic stability of such system is proposed. It is demonstrated that several previously reported stability criteria for two-dimensional (2D) systems are recovered from the presented approach as special cases. Numerical examples are given to illustrate the usefulness of the presented approach.

Stability Analysis for Generalized Neutral-Type Neural Networks

2011 ◽  
Vol 121-126 ◽  
pp. 1387-1391
Author(s):  
Guo Quan Liu ◽  
Simon X. Yang
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Condition ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Inequality Technique ◽  
Globally Stable

The issue of asymptotic stability is discussed for generalized neutral-type neural networks with time-varying delays. A new stability condition is presented based on the Lyapunov-Krasovskii method and the inequality technique, which is dependent on the amount of delay. The proposed result is given in the form of a linear matrix inequality (LMI). Finally, an example is given to illustrate our result. This result is of great significance in designs and applications of globally stable of generalized neutral-type neural networks.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

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